add kata

5kyu/common-denominators/description.md

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+Common denominators
+
+You will have a list of rationals in the form
+
+`{ {numer_1, denom_1} , ... {numer_n, denom_n} } `
+or
+`[ [numer_1, denom_1] , ... [numer_n, denom_n] ] `
+or
+`[ (numer_1, denom_1) , ... (numer_n, denom_n) ] `
+where all numbers are positive ints. You have to produce a result in the form:
+
+`(N_1, D) ... (N_n, D)`
+or
+`[ [N_1, D] ... [N_n, D] ]`
+or
+`[ (N_1', D) , ... (N_n, D) ]`
+or
+`{{N_1, D} ... {N_n, D}}`
+or
+`"(N_1, D) ... (N_n, D)"`
+depending on the language (See Example tests) in which D is as small as possible and
+
+`N_1/D == numer_1/denom_1 ... N_n/D == numer_n,/denom_n.`
+Example:
+`convertFracs [(1, 2), (1, 3), (1, 4)] `shouldBe` [(6, 12), (4, 12), (3, 12)]`
+Note:
+Due to the fact that the first translations were written long ago - more than 6 years - these first translations have only irreducible fractions.
+
+Newer translations have some reducible fractions. To be on the safe side it is better to do a bit more work by simplifying fractions even if they don't have to be.
+
+Note for Bash:
+input is a string, e.g `"2,4,2,6,2,8"` output is then `"6 12 4 12 3 12"`

5kyu/common-denominators/solution.ts

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+/**
+ * Finds the greatest common divisor of two numbers
+ * using Euclid's algorithm.
+ */
+const gcd = (a: number, b: number): number => {
+  return a === 0 ? b : gcd(b % a, a);
+}
+
+/**
+ * Finds the least common multiple of two numbers.
+ */
+const lcm = (a: number, b: number): number => {
+  return a * b / gcd(a, b);
+}
+
+/**
+ * Simplifies a fraction to its simplest form.
+ */
+const simplify = (numerator: number, denominator: number): [number, number] => {
+  const divisor = gcd(numerator, denominator);
+  return [numerator / divisor, denominator / divisor];
+}
+
+export const convertFrac = (lst: [number, number][]): string => {
+  const simplifiedList = lst.map(([numerator, denominator]) => simplify(numerator, denominator));
+  // find the least common multiple of all the denominators
+  const lcmDenominator = simplifiedList.reduce((acc, [_, denominator]) => lcm(acc, denominator), 1);
+  return simplifiedList
+    .map(([numerator, denominator]) => [numerator * lcmDenominator / denominator, lcmDenominator])
+    .map(([numerator, denominator]) => `(${numerator},${denominator})`)
+    .join('');
+}

5kyu/common-denominators/tests.ts

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+import { convertFrac } from './solution';
+import { assert } from "chai";
+
+describe("Fixed Tests", function () {
+  it("Basic tests convertFrac", function () {
+    assert.strictEqual(
+      convertFrac([[1, 2], [1, 3], [1, 4]]),
+      "(6,12)(4,12)(3,12)"
+    );
+    assert.strictEqual(
+      convertFrac([[69, 130], [87, 1310], [3, 4]]),
+      "(18078,34060)(2262,34060)(25545,34060)"
+    );
+    assert.strictEqual(
+      convertFrac([[1, 2], [4, 5], [3, 4], [6, 9], [7, 10]]),
+      "(30,60)(48,60)(45,60)(40,60)(42,60)"
+    );
+  });
+});